The cumulative frequency table above gives the information we need to complete a cumulative frequency diagram of the marks students received in a test. The Cumulative Frequency diagrams tell us about the data at a point and the data leading up to that point, so the cumulative frequency point for students with 50 marks tells us the number of student who received 50 and below, which is this case is 57 out of 60 students. This can also tell us that 3 out of 60 students received more than 50 marks in the test.
To calculate the Median from the CF diagram we go half way up the y axis to the n/2 th value so in this case as there are 60 students, the median is at the 30th value. By draw a horizontal line across from 30 until we hit the CF line we then drop a vertical line down until we hit the x axis and read the value from there, giving us a median value of 25 marks.
To caculate the Lower Quartile and Upper Quartile we follow a similar process but for the Lower Quartile we go up the y axis to find the n/4th value and the 3n/4th value for the Upper Quartile.
Giving solutions in this example of LQ = 15th value = 17 marks
and UQ = 45th value = 34 marks
From this we can calculate the interquartile range = UQ - LQ
In this example = 34 - 17 = 17 marks
Box plots are great at comparing data when we have calculated median, lower quartile, upper quartile and the upper and lower bounds of the data. We can see the distribution between two data sets to see if they are positively or negatively skewed and argue as to the outcome of the data by comparing 2 or more set of results.
The cumulative frequency table above gives the information we need to complete a cumulative frequency diagram of the marks students received in a test. The Cumulative Frequency diagrams tell us about the data at a point and the data leading up to that point, so the cumulative frequency point for students with 50 marks tells us the number of student who received 50 and below, which is this case is 57 out of 60 students. This can also tell us that 3 out of 60 students received more than 50 marks in the test.
To calculate the Median from the CF diagram we go half way up the y axis to the n/2 th value so in this case as there are 60 students, the median is at the 30th value. By draw a horizontal line across from 30 until we hit the CF line we then drop a vertical line down until we hit the x axis and read the value from there, giving us a median value of 25 marks.
To caculate the Lower Quartile and Upper Quartile we follow a similar process but for the Lower Quartile we go up the y axis to find the n/4th value and the 3n/4th value for the Upper Quartile.
Giving solutions in this example of LQ = 15th value = 17 marks
and UQ = 45th value = 34 marks
From this we can calculate the interquartile range = UQ - LQ
In this example = 34 - 17 = 17 marks
What does this tell us about the data?
Box and Whisker Diagrams (Box Plots)
Box plots are great at comparing data when we have calculated median, lower quartile, upper quartile and the upper and lower bounds of the data. We can see the distribution between two data sets to see if they are positively or negatively skewed and argue as to the outcome of the data by comparing 2 or more set of results.